RESEARCH AREA. Basic neuroscience involving structure/function relations for neuronal dendritic branching, dendritic spines, and synapses (also neuron populations with cortical symmetry), and for such functions as synaptic transmission, amplification and dendro- dendritic interactions in the context of spatio-temporal input patterns, logical processing of input, and neural plasticity, as in conditioning and learning. RATIONALE. Combine experimental data from neuroanatomy and from electrophysiology with biophysical models of nerve membrane (passive, synaptic and excitable) into a comprehensive theory which can lead to new insights and to testable theoretical predictions (leading to the design of better experiments). To do this we must create explore and test mathematical and computational models with different degrees of complexity. METHODOLOGY. Our methods include both analytical solutions and computational solutions of boundary value problems (for partial differential equations) in the tradition of classical physics. They include also the formulation and solution of problems in terms of systems of ordinary differential equations; when this is done explicitly for a compartmental model of a neuron, it is possible to accommodate a remarkable variety of dendritic branching patterns and non-uniform distributions of membrane properties and of synaptic inputs. RESULTS. Earlier results are summarized in Chapt. 3 of "The Handbook of Physiology: The NERVOUS System, Vol. 1" published by the American Physiological Society, 1977 (Kandel, Brookhart & Mountcastle, eds.). More recent results are described in Chapter 22 of "Synaptic Function", Wiley, 1987 (Edelman, Gall & Cowan, eds.).